The heterogeneous nature of a protein surface plays an essential role in its biological activity and molecular recognition, and this role is mediated at least partly through the surrounding water molecules. We have performed atomistic molecular dynamics simulations of an aqueous solution of HP-36 to investigate the correlation between the dynamics of the hydration layer water molecules and the lifetimes of protein -water hydrogen bonds. The nonexponential hydrogen bond lifetime correlation functions have been analyzed by using the formalism of Luzar and Chandler, which allowed identification of the quasi-bound states in the surface and quantification of the dynamic equilibrium between quasi-bound and free water molecules in terms of time-dependent rate of interconversion. It is noticed that, irrespective of the structural heterogeneity of different segments of the protein, namely the three a-helices, the positively charged amino acid residues form longer-lived hydrogen bonds with water. The overall relaxation behavior of protein-water hydrogen bonds is found to differ significantly among the three helices of the protein. Study of water number density fluctuation reveals that the hydration layer of helix-3 is much less rigid, which can be correlated with faster structural relaxation of the hydrogen bonds between its residues and water. This also agrees excellently with faster translational and rotational motions of water near helix-3, and hence the lower rigidity of its hydration layer. The lower rigidity of the helix-3 hydration layer also correlates well with the biological activity of the protein, as several of the active-site residues of HP-36 are located in helix-3.